This invention pertains to compositions useful in dental composites or in other composite materials, particularly to compositions that release fluoride ion and that may be recharged with additional fluoride ion.
Fluoride is the most widely used agent to prevent dental caries (tooth decay). Tooth decay can occur on the margins of dental restorations. Such recurring caries is a frequent cause for failure of dental restorations. Fluoride-releasing restorative materials have been used to try to reduce recurrent caries at restoration margins. The effectiveness of such fluoride-releasing materials varies widely. Fluoride-releasing materials generally fall into one of four categories: glass ionomers, resin-modified glass ionomers, compomers, and fluoride-releasing composite resins. In general, materials with higher levels of fluoride release tend to have poorer mechanical properties (e.g., a lower compressive strength) High fluoride-releasing materials have therefore been used clinically primarily to restore decayed, but non-biting areas.
Glass ionomers and resin-modified glass ionomers release fluoride as a by-product during acid-base reactions between the ion-leachable fluoride glass and an acidic liquid. Glass ionomers and resin-modified glass ionomers generally have high fluoride release and recharge capabilities, but they have low strength and poor esthetic qualities. Composite resins have been widely used in restorative dentistry because they have high strength, good wear resistance, and excellent esthetics, but they release relatively small amounts of fluoride, and have low fluoride-recharge capabilities. There is an unfilled need for dental composite resins with high strength, good wear resistance, high fluoride release rates, and high fluoride recharge capability.
Currently, fluoride released from resin-based dental restorative materials comes from four main sources: (1) a soluble free salt, such as NaF, KF, or SnF2 added to the material; (2) fluoride-releasing glass fillers such as fluoroaluminosilicate glass or sparingly soluble inorganic salts such as YbF3; (3) polymer molecules containing an anion-exchangeable fluoride moiety such as xe2x80x94N(CH3)2HF; (4) or organic fluoride sources such as those from alkylonium tetrafluoroborate.
U.S. Pat. No. 6,391,286 discloses fluoride releasing materials for use in dental compositions, having the formula M(G)g(F)n or M(G)g(ZFm)n, where M is an element capable of forming a cationic species and having a valence of 2 or more; G is an organic chelating moiety capable of complexing with the element M; Z is hydrogen, boron, nitrogen, phosphorus, sulfur, antimony, or arsenic; F is fluoride; and g, m, and n are at least 1.
U.S. Pat. No. 4,871,786 discloses dental compositions employing one or more substantially soluble organic compounds that serve as fluoride sources by incorporating tetrafluoroborate. Preferred non-polymerizable fluoride sources were said to be compounds of the formula: Rnxe2x80x94M+ BF4xe2x88x92 where M is I, N, P, or S; n is 2, 3, or 4, depending on the identity of M; and R is one of several specified types of substituted or unsubstituted hydrocarbon chains. Preferred polymerizable fluoride sources were said to be compounds of the formula: R(nxe2x88x921)xe2x80x94M+(L) BF4xe2x88x92 where the other symbols were as previous stated, and L is an organic ligand comprising a moiety capable of polymerization via a cationic, condensation, or free radical mechanism.
Published international patent application WO 00/69394 discloses what were said to be stable one-part dental materials comprising a compound having only one acid functionality and at least one polymerizable functionality on each compound. The material does not contain storage-deleterious quantities of polyacid compounds. The material also contains a fluoride source containing polyvalent metal ions, and a photopolymerization initiator.
A Yuchi et al., xe2x80x9cComplexes of Hard Metal Ions with Amine-N-Polycarboxylates as Fluoride Receptors,xe2x80x9d Bull. Chem. Soc. Jpn., vol. 69, pp. 3173-3177 (1996) discloses studies of equilibria in the reaction of hard metal complexes (Mm+: Al3+, Zr4+, Hf4+, Th4+; HnL: amine-N-polycarboxylic acid) with fluoride. The zirconium (IV) complex of N-methyliminodiacetic acid was reported to be an excellent fluoride receptor.
M. Chikuma et al., xe2x80x9cSelective Sorption of Fluoride Ions by Anion-Exchange Resin Modified with Alizarin Fluorine Blue-Praseodymium (III) Complex,xe2x80x9d Reactive Polymers, vol. 13, pp. 131-138 (1990) disclosed a resin for the selective sorption of fluoride ion, prepared from an anion exchange resin, Amberlite IRA 400, and a praseodymium (III) complex of alizarin fluorine blue.
H. Rawls et al., xe2x80x9cEsthetic Materials with Active Agent Control Release Capabilities and Their Future Roles,xe2x80x9d pp. 130-135 in Symposium on Esthetic Restorative Materials, 1991 (American Dental Association 1993) provides a review of dual-purpose dental restorative materials: those that can serve the needs of esthetic dentistry and that can also serve as sustained-release sources of therapeutic agents, such as fluoride. See also H. Rawls, xe2x80x9cPreventive Dental Materials: Sustained Delivery of Fluoride and Other Therapeutic Agents,xe2x80x9d Advances in Dental Research, vol. 5, pp. 50-55 (December 1991).
A. Peutzfeldt, xe2x80x9cResin Composites in Dentistry: The Monomer Systems,xe2x80x9d Eur. J. Oral Sci., vol. 105, pp. 97-116 (1997) provides a general review of dental resin monomers and composites, including some that release fluoride.
E. Glasspoole et al., xe2x80x9cA Fluoride-Releasing Composite for Dental Applications,xe2x80x9d Dental Materials, vol.17, pp. 127-133 (2001) discloses the incorporation of an organic fluoride material, tetrabutylammonium tetrafluoroborate, into a hydrophilic monomer system made of 2,2-bis[4-(2-hydroxy-3-methacroyloxypropoxy)phenyl]-propane and 2-hydroxyethyl methacrylate. Resulting fluoride release rates were reported to exceed those of several glass ionomer materials that were also tested.
B. Zimmeran et al., xe2x80x9cPrevention of in vitro Secondary Caries with an Experimental Fluoride-Exchanging Restorative Resin,xe2x80x9d J. Dental Res., vol.63, pp. 689-692 (1984) reported clinical observations in which experimental composite resins that released fluoride by ion exchange were seen to reduce the incidence of caries in immediately adjacent areas, as compared to the rates of caries observed when non-fluoride-containing materials were used.
We have discovered novel fluoride-releasing compositions that may be incorporated into dental composite restorative materials or other dental materials, to produce materials with high fluoride release rates and high fluoride recharge capability. Such resins may be used, for example, in dental restorative materials to help reduce the level of dental caries in patients, particularly the level of caries occurring on the margins of the restorative materials.
The novel chelating and fluoride-releasing monomers may be described by the following general formulas, where the first formula below depicts a chelating monomer, and the second depicts the monomer chelated to a metal atom, which in turn is coordinated to one or more fluoride ions: 
where R1 is a substituted or unsubstituted aliphatic or aromatic group having 2 to 24 carbon atoms, and having at least one polymerizable group, the polymerizable group being preferably, but not necessarily, located in a terminal position; R2 is a substituted or unsubstituted aliphatic or aromatic group having 2 to 50 carbon atoms; M is a metal atom having a valence of +2 or higher; R3 and R4 are unidentate or multidentate ligands that can form a coordination bond or ionic bond with M; R3 and R4 can be the same or different, but at least one them is a multidentate (at least a bidentate) ligand; i, j, l, and n are positive integers; F is a fluoride atom; Z is a counter-ion to maintain the neutrality of the monomer; and m is an integer from 0 to 4.
One advantage of having two coordinating ligands, R3 and R4, is that the combination forms a more stable chelate with the metal, which can help minimize the loss of metal ion from the material under conditions of use.
Preferred embodiments of the invention include one or more of the following options: (1) the use of multiple polymerizable terminal groups in the R1 moieties, such as di- or polymethacrylates, to form a cross-linked polymer matrix with better mechanical properties and lower monomer loss than typically occurs with metallofluorocomplexes containing one or zero polymerizable groups; (2) adjusting the spatial arrangement of R3 and R4 by, for example, changing the length of one of the ligands to optimize formation of the fluoride-metal chelate and the later release of fluoride from the chelate; (3) multinucleate metal chelates (i.e., a single monomer structure containing more than one metal atom), which can increase the fluoride release and recharge capability.
This invention provides a class of polymerizable monomers containing chelating groups and fluoride-exchanging metal chelates that can release fluoride into an aqueous solution, and that can xe2x80x9crechargexe2x80x9d by taking up fluoride from an aqueous solution containing a high concentration of fluoride (e.g., a fluoridated toothpaste or mouthwash).
In the general formula above, M is a metal having a valence of +2 or greater. Preferred metals M are those having +3 or +4 valences, particularly those that tend to form colorless complexes with the ligands and with fluoride. For example, M may be Sn+2; Zn+2, Sr+2, Al+3, La+3, Ce+3, Sb+3, Yb+3, Ti+4, Sn+4, Zr+4, Ce30 4, or Th+4. Particularly preferred is Zr+4, because that cation is nontoxic, colorless, relatively inexpensive, has a high valence, and has a high tendency to form multinucleate complexes with fluoride ions, leading to high fluoride-exchange capacity. In addition, Zr has a high atomic weight, providing radiopacity, a desirable property for dental restorative materials. Z is a counter ion to maintain the neutrality of the monomer, for example hydrogen, lithium, sodium, potassium, ammonium or quaternary ammonium. Preferred Z include hydrogen or sodium.
The R1 group contains at least one polymerizable moiety such as a Cxe2x95x90C double bond, an expoxy group, an ethyleneimine group, etc. Preferred R1 groups include the esters of acrylic or methacrylic acid. Specific examples include methyl acrylate, methyl methacrylate, ethyl acrylate, ethyl methacrylate, propyl acrylate, propyl methacrylate, isopropyl acrylate, isopropyl methacrylate, 2-hydroxyethyl acrylate, 2-hydroxyethyl methacrylate, hydroxypropyl acrylate, hydroxypropyl methacrylate, tetrahydrofurfuryl acrylate, tetrahydrofurfuryl methacrylate, glycidyl acrylate, glycidyl methacrylate, glycerol mono- and di-acrylate, glycerol mono- and di-methacrylate, ethyleneglycol diacrylate, ethyleneglycol dimethacrylate, neopentyl glycol diacrylate, neopentylglycol dimethacrylate, and trimethylolpropane triacrylate.
Other suitable examples of R1 include vinyl azalactone, vinyl pyrrolidone, styrene, divinylbenzene, urethane acrylates or methacrylates, epoxy acrylates or methacrylates and polyol acrylates or methacrylates, substituted acryl amides and methacrylamides.
Alternatively, the polymerizable component may be a cationically curable material, such as one of the epoxies, oxetanes, oxolanes, cyclic acetals, lactams, lactones, vinyl ethers, and spirocyclic compounds containing one or more oxygen atoms in the ring.
R2 is a substituted or unsubstituted aliphatic or aromatic group containing 2 to 50 carbon atoms. The structure of R2 should permit the bonding of at least four functional groups (two R1, an R3, and an R4). Preferred R2 groups are derivatives of aromatic diols, diacids, and diepoxides, such as substituted or unsubstituted bisphenols, hydroquinone, diphenols, and dihydroxyphthalic acid. Other suitable examples for R2 include aliphatic diamines such as polyethylenediamines and polyethyleneglycodiamines, and derivatives of citric acid, tartaric acid, cyclohexane, cyclopentane, tetrahydrofuran, and tetrahydropyrrole. The structures of preferred R2 groups are illustrated by the general formulas: 
where X is hydrogen or a substituted or unsubstituted alkyl group having from 1 to 12 carbon atoms, such as methyl, ethyl, propyl, isopropyl, butyl, or t-butyl. Y is C(CH3)2, CH2, O, CO, S, SO2, or CH3CCH2COOH. The value of n is an integer from 1 to 12.
R3 and R4 are unidentate or multidentate ligands that can form coordination bonds or ionic bonds with M. R3 and R4 are covalently bonded to R2. R3 and R4 can be the same or different, but at least one of them should be at least a bidentate or multidentate ligand capable of forming a 4-8 member ring when chelating the metal ion M. Preferred structures for R3 and R4 have a combined ligand number of 3 or 4 (not counting the bonds to the fluoride, or the coordination bonds formed by the lone electron pairs from N, O, S, etc.).
A wide variety of ligands may be used for R3 and R4. Examples of multidentate ligands include substituted carboxylic di-acids or tri-acids and their salts, such as aminodiacetic acid, amidodiacetic acid, benzyliminodiacetic acid, phthalic acid, salicylic acid, citric acid, tartaric acid, hydroxamic acid, cyclohexen-1,2-diacid, phosphoric acid, aminophosphoric acid, phosphonic acid, and 8-hydroyquinoline. Examples of unidentate ligands include compounds with a hydroxyl group, such as alcohols; carboxylic acids; and a half ester (derived from an anhydride or chloride) of an aliphatic or aromatic diacid having from 2 to 12 carbon atoms, such as oxalic acid, malonic acid, maleic acid, a disubstituted maleic acid, succinic acid, fumaric acid, malic acid, tartaric acid, glutaric acid, glutaconic acid, adipic acid, pimelic acid, cyclohexen-1,2-diacid, (o, m, or p)-phthalic acid, citric acid, hydroxyphthalic acid, suberic acid, trimellitic acid, sebaric acid, and their salts.
Particularly preferred chelating monomers are compounds containing aminodiacetic acid, amidodiacetic acid, phosphonic acid, or aminophosphoric acid groups, and having a molecular weight between 100 and 2000, for example, one of the following structures M1 to M20: 
where X is hydrogen, or a substituted or unsubstituted alkyl group having from 1 to 12 carbon atoms such as methyl, ethyl, propyl, isopropyl, butyl, or t-butyl. Using an alkyl group as X will help reduce the hydrophilicity of the monomer, and can help inhibit unwanted substitution reactions. Y is a pendent group that may or may not participate in chelate formation. The simplest Y is hydrogen, which does not participate in chelate formation; and a typical Y is a hydroxyl group, which can participate in chelation. Y may also be, for example, an ester of a phosphoric acid, or a half ester of an aliphatic or aromatic diacid or triacid having from 2 to 12 carbon atoms, such as oxalic acid, malonic acid, maleic acid, a disubstituted maleic acid, malic acid, succinic acid, fumaric acid, malic acid, tartaric acid, glutaric acid, glutaconic acid, citric acid, adipic acid, pimelic acid, cyclohexen-1,2 diacid, (o, m, or p)-phthalic acid, hydroxyphthalic acid, suberic acid, trimellitic acid, or sebaric acid. The chain length of such a diacid or triacid may be selected to optimize the formation of the fluoride-exchange metal chelate and the release of fluoride thereof. The various X groups depicted in the above structures may be the same as, or different from one another, as may the various Y groups. The number n is an integer from 0 to 12.
Following are preferred synthetic schemes for synthesizing the preferred monomers for use in the present invention
(1) Add a chelating ligand to R2 which is an aromatic diol, such as a substituted or unsubstituted bisphenol, diphenol, or hydroquinone.
(a) Iminodiacetic acid undergoes a Mannich-type reaction with R2 and formaldehyde or polyformaldehyde in an aprotic polar solvent such as DMF or dioxane at 80xc2x0 C. for several hours to overnight. This process generates precursors for monomers such as M1, M6, and M11, where Y is not hydrogen and n is at least 1.
(b) For a precursor to M1, diethyl iminodiacetate may be used instead, followed by reaction with bromoethanol or ethylene carbonate to add xe2x80x94O(CH2)2OH groups, then hydrolysis with K2CO3/NaOH, and acidifying with HCl.
(c) To add aminophosphoric groups (e.g., M4, M5, M7, and M8), R2 first undergoes a Mannich-type reaction with CH2O and NH3, then reacts with CH2O and PCl3 or HP(O)(OCH2CH3)2, followed by hydrolysis. For monomers M4, M7, M9, M14 and M17, the amount of PCl3 or diethyl phosphite should be controlled so that only one phosphite group attaches to the amine. Then the secondary amine may be converted into a tertiary amine through an Eichweich-Clark reaction, i.e. reduction by formic acid in the presence of formaldehyde (Xxe2x95x90CH3).
(d) To add chelating groups to R2 through amide groups (e.g., M2, M9, M10, M19, and M20), the carboxylic acids on R2 first react with iminodiacetic acetate (for M2 and M10) or NH3 (for M9, M19, and M20) in 1,4-dioxane in the presence of 1-methyl-2-chloropyridiniumiodide and triethylamine at room temperature, followed by hydrolysis with K2CO3/NaOH, and acidifying with HCl to yield precursors of M2 and M10, or reaction with CH2O and PCl3 to yield a precursor of M9.
(e) To add phosphonic acid groups (e.g., M3 and M12), 3,3xe2x80x2-dimethyl-bisphenol A or diphenol is first reacted with bromoethanol or ethylene carbonate to add xe2x80x94O(CH2)2OH groups; and then reacted with pyridinium tribromide (CH5NH)Br3 to convert the methyl group to xe2x80x94CH2Br, which further reacts with P(OCH3)3 or (POCH2CH3)3 to form a methyl phosphonate, which can later be hydrolyzed to a phosphonic acid with trimethylsilyl bromide and a methanol/water mixture.
(2) Add a polymerizable terminal group R1 (e.g., a methacrylate).
(a) The above precursors with chelating groups will react with 2,3-epoxypropyl methacrylate or 2,3-epoxyalkyl methacrylate (alkyl containing 3 to 12 carbon atoms) in 1,4-dioxane at 100xc2x0 C. for 24 hours to add a hydroxypropyl methacrylate or hydroxyalkyl methacrylate to each phenol group (Y=OH). Monomers M1 to M12, M19, and M20 may be prepared in this way from the precursors generated in step (1).
(b) For the special case where Y is a hydrogen (i.e., no pendent Y group), a methyl or ethyl ester of the chelating group (e.g., iminodiacetic acid or phosphoric acid) may be used in step (1). Then the resulting precursors may react first with bromoalcohol or ethylene carbonate (n=0) to add (CH2)n+2OH (n=0 to 12), followed by hydrolysis to convert the esters of the chelating groups to the acids. Then the resulting products react with methacryloyl chloride in DMF or 1,4-dioxane.
(3) M13 to M18 may be prepared as follows: first, the sterically less hindered amino group of (D,L)-lysine is selectively acrylated by reaction with benzyl cyanoformate, followed by reaction with bromoacetic acid (for M13 and M16) or PCl3, followed by hydrolysis (for M14, M15, M17, and M18). Removal of the benzyl protecting group will proceed in high yield by hydrogenolysis. The product further reacts with 1-chloromethyl-4-vinylbenzene to yield M13, M14, and M15; or with methacryloyl chloride to yield M16, M17, and M18.
(4) The pendent hydroxyl group (Y) may be converted to a stronger ligand, such as a phosphoric acid ester, or a half ester of an aliphatic or aromatic diacid or triacid having from 2 to 12 carbon atoms, by reaction with the corresponding anhydrides or chlorides followed by hydrolysis. Specific examples of such diacids or triacids include oxalic acid, malonic acid, maleic acid, disubstituted maleic acid, malic acid, succinic acid, fumaric acid, malic acid, tartaric acid, glutaric acid, glutaconic acid, tartaric acid, citric acid, adipic acid, pimelic acid, cyclohexen-1,2 diacid, (o, m, or p)-phthalic acid, suberic acid, trimellitic acid, and sebaric acid. The chain length of the diacid may be selected to optimize formation of the fluoride-exchanging metal chelate, and the release of fluoride from the chelate.
The preferred fluoride-releasing monomers may be prepared from chelating monomers such as those described above and metal fluorides. Methods of preparation include the following three:
(1) The acidic chelating monomers are reacted directly with a metal fluoride in a polar organic solvent such as methanol, DMF, or tetraethyleneglycol dimethacrylate. This process is easy to carry out, but can be slow (e.g., 1 to 7 days), unless the metal fluoride has substantial solubility in the solvent.
(2) The acidic chelating monomers are first reacted with metal salts that are partially soluble in the organic solvent, e.g., nitrates or acetates, and then fluoride is added, e.g., as. HF, NaF, NH4F, LiF, or a tetraalkyl ammonium fluoride such as (CH3)4NF, (C2H5)4NF, or [CH3(CH2)3]4HF.
(3) First, a metal fluoride salt, e.g., ZrF4, is dissolved in concentrated hydrofluoric acid (HF) or a mixture of HF with a fluoride salt such as NaF, NH4F, LiF, [CH3(CH2)3]4NF, etc. The resulting solution containing metal-fluoride complexes, such as [ZrF5]xe2x88x92 or [Zr2F9]xe2x88x92, then reacts with the monomer-methanol solution. This reaction is fast at room temperature, and is therefore is the most efficient of the three methods; but it is only useful for those metals (e.g., Zr, Al) that form anionic fluoride complexes that are soluble in water and methanol. The excess HF and unreacted metal-fluoride complexes can be removed by evaporation and absorption with Ca(OH)2, followed by redissolving the product in an organic solvent, such as isopropanol, in which Zrxe2x80x94F complexes will precipitate.
Some examples of fluoride-releasing monomers formed using such chelating monomers, zirconium, and fluoride are shown in the following structures: 
The chelating monomers and fluoride-releasing monomers may be dissolved in, or mixed with, monomers or mixtures of monomers known in the art for use in dental materials, such as bisphenol A glycidyl dimethacrylate, hydroxyl ethyl methacrylate, triethyleneglycol dimethacrylate, and urethane dimethacrylate. The amount of the fluoride-releasing monomers may be from about 0.1% to about 70% by weight of total monomers, depending on the requirements for fluoride release and other physical and mechanical properties, the preferred ratio being from about 20% to about 40%. The monomer mixtures may be polymerized (cured) by means known in the art, such as free radical reactions initiated by photoinitiators or chemical initiators. Such photoinitiators include diketones such as camphorquinone, and 1-phenyl-1,2-propanedione (PPD). Chemical initiators are usually organic peroxides such as benzoyl peroxide. Reducing agents or accelerators may also be added, such as aliphatic or aromatic tertiary amines, for example dimethylaminoethyl methacrylate. The total ratio of initiators and accelerators is typically between about 0.03% and about 5% by weight of total materials, with a preferred range between about 0.3% and about 1%.
The chelating monomer, fluoride-releasing monomers and their mixtures with other monomers may be used with or without fillers. Preferred compositions for dental composite resins contain both fluoride-releasing monomers and fluoride-releasing filler particles such as a fluoroaluminosilicate glass, for example, that described in U.S. Pat. No. 5,332,429. The fillers may also include other inorganic compounds such as SiO2, ZrO2, TiO2, ZrF4, NaF, AlF3, LiF, SrF2, CeF3, Ca3(PO4)2, La2O3, Ce2O3 and glasses incorporating these compounds. Preferred particle sizes for fillers are 0.1 to 5 micrometer, more preferably 0.2 to 3 micrometer.
To enhance bonding between the filler and the resin matrix, the filler surface is preferably treated with a silane coupling agent, such as xcex3-methacryloyl-oxypropyltrimethoxysilane, xcex3-mercaptopropyltriethoxysilane, xcex3-aminopropyltrimethoxysilane, and O-(methacryloxyethyl)-N-(triethoxysilylpropyl)urethane. Alternatively, the filler particles may be treated with an organic acid containing polymerizable functional groups, including for example the chelating monomers of the present invention. The filler load varies by type of application: for example, it can range from about 5% to about 50% in a sealant or a filled dental adhesive, from about 40% to about 60% for flowable composites, and up to about 85% for posterior composites.
Applications for the chelating monomers and fluoride-releasing monomers of the present invention include, for example, dental restorative materials such as composite resins, compomers, resin-modified glass ionomers, sealant, liners, cements, provisional/temporary materials, dental adhesives (bonding agents), denture base resins, and orthodontic adhesives.
Alternatively, polymers and composites made from the novel chelating monomers and their metal chelates may also be used in the preparation of ion exchange resins, which may be used, for example, in the separation of metals, fluoride ions, and other anions by chemical manufacturers or analytical laboratories; or in the removal of hazardous metals or unwanted fluoride from industrial waste water. The chelating monomers may also be used to coat metal surfaces including dental and medical implants to enhance protection or bonding.
The following examples are presented to demonstrate the synthesis, fabrication, and testing of materials in accordance with the present invention. These examples are not intended to limit the scope of the invention in any way. All starting materials are commercially available (most of them from Sigma-Aldrich). IR spectra were recorded on a Bio-Rad FTS-40 FT-IR spectrometer. NMR spectra were measured on an Inova-500 (1H and 13C) NMR spectrometer, 1H at 500 MHz, 13C at 125 MHz, using TMS as an internal standard. The F19 NMR chemical shift was expressed relative to the position of the trifluoride toluene signal as 33.858 ppm. Electrospray mass spectrometry (ES-MS) was carried out on a Bruker Daltonics Esquire 3000 Ion Trap Electrospray Mass Spectrometer. In the formulas given for the assignment of mass spectra peaks, such as [Mxe2x88x924H+Zr+F]xe2x88x92, M is the mass of the chelating monomer or its precursor; H, Zr, F are the mass of the most abundant isotope of hydrogen, zirconium, and fluorine, respectively. (I.e., H=1.00, Zr=89.90, F=19.00.) Zirconium has a unique isotope distribution (Zr90 51.45%, Zr91 11.27%, Zr92 17.17%, Zr94 17.37%, Zr96 2.78%), which can be used to identify its presence and abundance in a chelate. Note that some syntheses were run in more than one batch, although only one batch is reported below; hence the starting amount of a particular compound in a later synthetic step may sometimes appear to be more than was synthesized in an earlier step.